Simulation of piano strings and a soundboard by a large deformation theory

Abstract

Three-dimensional finite element analyses of piano strings and a soundboard are presented in which a large deformation theory is adopted. In the large deformation theory, the momentum balance of a body is preserved in the course of the deformation and the changes of direction and amplitude of axial force due to deformation are taken into account. It is shown that the secondary partials appear in the spectrum of the velocity component in the axial direction as well as the transverse direction. A hammer is modeled by masses with springs and dashpots. Gap elements are employed to simulate the contact and detachment between the hammer model and a string. It is demonstrated that multiple reflections between hammer and agraffe can be reproduced by the method. Modeling of the interaction among strings, a bridge, and a soundboard is also discussed in which the crown and the preloading of the soundboard are taken into account.